L'aire des triangles ideaux en geometrie de Hilbert
Differential Geometry
2009-09-29 v1 Metric Geometry
Abstract
In this paper we study the area of ideals triangles in a convex domain with its Hilbert geometry. We obtain a characterization of the hyperbolic geometry among all the Hilbert geometry in terms of area of ideals triangles. We also obtain a sharp lower bound on the hilbert area of ideal triangles, independant of the convex, which characterizes the triangle domains in the plane. Furthermore, under specific geometric assumptions, we obtain an upper bound, which depends on the convex domain.
Cite
@article{arxiv.math/0312163,
title = {L'aire des triangles ideaux en geometrie de Hilbert},
author = {Bruno Colbois and Constantin Vernicos and Patrick Verovic},
journal= {arXiv preprint arXiv:math/0312163},
year = {2009}
}
Comments
32 pages, 16 figures